Fredrik Fors Mechanical Engineering, JLab 04/22/2016 RFD Cavity Tuner Attachment for the HF-LHC project at CERN, through US-LARP Structural Analysis Fredrik Fors Mechanical Engineering, JLab 04/22/2016

Summary Structural analysis of the tuner attachment of the RFD Crab Cavity being developed by Niowave Inc. for the High Luminosity LHC project at CERN Purpose is to evaluate the stresses induced in the cavity wall and the circumferential weld seam during tuner operation at cryogenic temperature. Both compressive and pulling tuner action is analyzed Two alternative designs for the tuner attachment have also been analyzed. The analysis is performed on 3D finite element models using ANSYS Workbench 17.0

Analyzed Geometry The RFD crab cavity consists of a 4 mm thick RRR Niobium shell, fitted with tubular flanged waveguides, stiffeners and tuner attachments. The CAD geometry used for the model was supplied as a STEP file from Niowave The round, bell shaped tuner attachments are welded to the top and bottom surface of the cavity and tune the cavity by pressing on the cavity wall. This is done symmetrically from both sides. Tuner attachment is fitted into a recess on the cavity wall and then EB welded around the edges. Tuner attached by M10 titanium Helicoil thread insert. Helicoil Tuner attachment Tuner attachment

Alternative Designs Two alternative designs of the tuner attachment have also been tested. Alternative design by JLab of the upper surface to reduce the stresses in the lower fillet of the original design Further adjusted design by Niowave to minimize the machining on the cavity surface. Tuner attachment is fitted in 2 mm deep circular groove rather than a full recessed surface. The reason is to minimize the machining and removal of material from the cavity wall. Alternative 1: Lower fillet retained but increased in size Stepped design replaced by conical Alternative 2: Similar to Alt. 1 but with redesigned fitting to cavity

FEA Model A section of the full cavity model was isolated and adapted for use in the FE Model. Regions of the cavity that were not considered to be structurally affected by the tuning were left out. The geometry is meshed with 2nd order tetrahedron elements. The mesh is greatly refined in the area of interest around the welded surface (0.2 mm), and gradually coarsens to ~4 mm at the model boundary.

Material Properties Material data for the RRR Niobium is same as used in an earlier CERN report1: Density ρ = 8600 kg/m3 Elastic Modulus E = 100 GPa Poisson’s Ratio ν = 0.4 Stress limits for the cavity are specified in the previous Crab cavity review by CERN2 Limit Stress Slim = 333 MPa (400 MPa with 1.2 safety factor) This in approximate correlation with Nb material data used at JLab. Following table is a summary from a JLab Technote3 Properties Value (@ RT) Density [kg/m3] 8570 Specific Heat [kJ/kg] 0.268 CTE [m/m/K] 7.1×10-6 Young’s modulus, [GPa] 105 Shear Modulus [GPa] 38 Poison’s Ratio [ - ] 0.38 Yield Stress [MPa] 405-897 (@ 4.2 K) Crab Cavity Stress Analysis v.1, 24/02/2014, Norbert Kuder, EN-MME-DI, CERN CRAB Cavities Cryomodule Review - Tuner, Kurt Altoon, Rama Calaga, et al. On Niobium in Construction of Cryogenic Pressure Vessel Systems, 2009, Gary Cheng, Edward Daly, JLab

Boundary Conditions Cut along horizontal plane treated as symmetry plane. The cavity is not completely symmetric but can be assumed so for the purpose of the analysis Waveguide openings are left without BC’s since they are far away from the area of interest. A vertical force of 2000 N is applied by means of a rigid MPC to the inner threaded surface of the tuner attachment. Helicoil not included in FE model. Surfaces forming the EBW joint between the tuner attachment and cavity are directly connected node to node. Frictionless contact applied on “bottom” surface of tuner attachment. Connected weld surfaces Force application Directly connected surfaces Frictionless contact surfaces

FEA Results – Original design High localized stresses occur in the cavity wall around the upper edge of the welding. Local maximum at edge Smax = 256 MPa Stress level 0.5 mm from edge S0.5mm = ~140 MPa (compensates for idealized sharp corner) Stress level at fillet Sfil = ~200 MPa Displacement at force application point: 0.38 mm Assuming Sfil vs. max allowable stress of 333 MPa, these results give: Max Tuner Force Ft,max = 333 / 200 * 2.0 = 3.33 kN Max. cavity deflection dmax = 333 / 200 * 0.38 = 0.63 mm (1.27 mm total) Tuning range Δfmax = 0.280 * 0.63 / 0.4 = 0.443 MHz (0.886 MHz total) Sfil Smax

FEA Results – Alternative 1 High localized stresses occur in the cavity wall around the upper edge of the welding. Local maximum at edge Smax = 237 MPa Stress level 0.5 mm from edge S0.5mm = ~130 MPa (compensates for idealized sharp corner) Stress level at fillet Sfil = ~120 MPa Displacement at force application point: 0.36 mm Assuming Sfil vs. max allowable stress of 333 MPa, these results give: Max tuner force Ft,max = 333 / 120 * 2.0 = 5.55 kN Max. cavity deflection dmax = 333 / 120 * 0.36 = 1.00 mm (2.00 mm total) Tuning range Δfmax = 0.280 * 1.0 / 0.4 = 0.699 MHz (1.40 MHz total) Sfil Smax

FEA Results – Niowave Alternative High localized stresses occur in the cavity wall around the upper edge of the welding. Local maximum at edge Smax = 312 MPa Stress level 0.5 mm from edge S0.5mm = ~170 MPa (compensates for idealized sharp corner) Stress level at fillet Sfil = 100 MPa Displacement at force application point: 0.365 mm Assuming Sfil vs. max allowable stress of 333 MPa, these results give: Max tuner force Ft,max = 333 / 100 * 2.0 = 6.66 kN Max. cavity deflection dmax = 333 / 100 * 0.365 = 1.22 mm (2.43 mm total) Tuning range Δfmax = 0.280 * 1.22 / 0.4 = 0.85 MHz (1.70 MHz total) Smax

FEA Results – Weld Stress As a complement to the analysis recently performed by Norbert Kuder at CERN4, the local stress intensity of a cross section line of the weld joint for the design alternatives have been extracted. His conclusion was that, for the original tuner attachment design, the stress level in the weld joint was acceptable but that the local stress in the fillet was too high. This analysis shows that the design alternatives have lowered the fillet stress significantly. The plot below shows a comparison of the weld stress intensity for the JLab design alternative, as well as the Niowave redesign. The plotted results are scaled to a tuner force of 7 kN. Also note that the weld seams is only 2 mm deep for the Niowave redesign option. 4. RFD tuner weld calculations - Norbert Kuder, CERN (EN-MME), 04/04/16

Comments Compared to the original tuner design, this analysis shows that the alternative designs offer substantial improvements of the stress level at the external fillet, with similar weld stress results. From a stress point-of-view, the recommendation is to proceed with the Niowave Alternative as the design for the tuner attachment of the RFD Cavity The calculation of max tuner force, max cavity deflections, and tuning range are derived from a previous analysis by CERN**. The results are simply scaled for current stress and deflection values. ** CRAB Cavities Cryomodule Review - Tuner, Kurt Altoon et al.